I hear that there are still some Texas folks that insist - INCORRECTLY - that a player that has his helmet come off illegally during a down when times expires for a period may participate in the first down of the next period. WRONG! WRONG! WRONG! That is just plain wrong, no matter who told you.
I wasn't there, but I understand that RR HIMSELF stated this at the TASO meeting. The rule states that he must sit out the next down, and there are no stated exceptions. But, if you need hard, written proof, just look at 2012 NCAA Play Interpretations Bulletin No. 1, play 6:
Helmet Off
6. Late in the first quarter ball carrier A22 is legally tackled, and his helmet comes off just after his back hits the ground. The game clock reads 0:00.
RULING: A22 must leave the game for the next down, which will be the initial down of the second quarter. A22’s helmet came off through play and there was no helmet foul by Team B. (3-3-9-a)
And no, halftime doesn't change anything. If his helmet comes off through play on the last down of the second period, he sits out the opening kickoff of the third period.
Not sure it gets any clearer.